Question

Use the conditional: If $\overline{AB}$and $\overline{CD}$intersect, then $\overrightarrow{AB}$and $\overrightarrow{CD}$intersect.

Point M is the midpoint of $\overline{RT}\cdot RM=x$, and $RT=4x-6$. Find the value of x.

Short answer

The number 3 represents the required value.

Step-by-step solution

Step 1. Observe the given information.

The provided information represents that the point M represents itself as the midpoint of $\overline{RT}$.

Step 2. Make an equation to determine the value of x.

The midpoint theorem can be used to determine the value of x. So, by using this make an equation.

$RM=\frac{1}{2}RT$

Step 3. Determine the value of x.

Substitute the given value of RM and RT into the obtained equation after it performs the simplification.

$x=\frac{1}{2}\left(4x-6\right)$

$x=2x-3$

$x=3$